Device for forming a field intensity pattern in the near zone, from incident electromagnetic waves

ABSTRACT

The present disclosure concerns a device for forming a field intensity pattern in the near zone, from electromagnetic waves which are incident on said device. Notably, such a device allows confining electromagnetic waves, which are incident on the device, into beams of radiation in the near zone. It comprises at least one layer of dielectric material, which surface has at least one abrupt change of level forming a step. A lower and lateral part of said surface with respect to said step is in contact with a substance having a refractive index lower than that of said dielectric material. For an incident electromagnetic wave impinging upon the device in the vicinity of such a step, the corresponding step of index it encounters produces a complex electromagnetic phenomenon, which allows generating low-dispersive condensed beams and specific field patterns in the near zone.

1. FIELD OF THE INVENTION

The present disclosure relates generally to techniques for forming fieldintensity patterns from electromagnetic waves, among which visiblelight. More particularly, but not exclusively, the present disclosurerelates to techniques for near-field focusing and beam forming in thenear zone. By near zone, it is meant here, and throughout this document,a region around a device according to the present disclosure, whosedimensions can extend from a fraction of the wavelength to about tenwavelengths in the host medium.

2. BACKGROUND

The focusing and collimation (i.e. beam forming (which can of coursealso be de-focusing)) of electromagnetic waves is an established way toincrease locally the magnitude of the electric field and, in such a way,enhance efficiency of sensors, e.g. electro-optical sensors whoseoperational principles rely on the conversion of the energy propagatingin space in the form of an electromagnetic wave into an output voltageor current. The latter sensors (for instance CMOS imaging sensors orphotodiodes) are in the heart of almost every portable electronicdevice, from smart-phones and tablets to professional light fieldcameras. The same phenomenon of local field enhancement is used in avariety of other applications in different wavelength ranges.

In the optical field, today level of technologies enables manufacturingof highly-integrated components (e.g. chips and optical sensors) withstructural elements having nano-scale dimensions, which are close to oreven smaller than the wavelength of visible light. The possibility ofmanipulating light with the same level of accuracy would be a greatbreakthrough compared to the state of the art.

However, the spatial resolution of conventional focusing devices, suchas dielectric and metal-dielectric lenses, is limited by the Abbediffraction limit and typically does not exceed one wavelength in thehost media. At the same time, there are many applications which require,or can benefit from, a sub-wavelength resolution, as explained by A.Heifetez et al. in “Photonic nanojets”, J. Comput. Theo. Nanosci., vol.6, pp. 1979-1992, 2009. This explains a growing interest for focusingcomponents enabling a sub-wavelength resolution.

Another critical challenge associated with the today mobile and wearabletechnologies consists in the need for further miniaturization of theassociated devices. The operational principles of the conventionallenses prevent reduction of their dimensions beyond a certain limit(^(˜)10 wavelengths) that constitutes a bottleneck for the futureadvances in the field. In particular, such a constraint may concern thepackaging density of light detectors and may thus handicap furtherimprovement of the image resolution.

Finally, the operational principles of the conventional lenses require acertain refractive index ratio between the lens and host mediummaterials. The higher the index ratio, the higher the lens focusingpower that can be achieved. Because of this, in most cases the lensesare separated by air gaps, which require additional space and causecertain difficulties with lens fixation in space and alignment. Fullyintegrated systems can help avoid these problems. However, combinationof several dielectric materials with different refractive indexes israther difficult and not always feasible because of both thetechnological difficulties and the limited range of the refractive indexvariation for the optically transparent materials (typical index valuein the optical range is n<2).

There is thus a need for new focusing components, which would overcomethese drawbacks.

However, at present, the most popular focusing elements remain convexdielectric lenses introduced long ago, as shown in FIG. 1A. Such a lenscan effectively focus light in a tight focal spot FS located at acertain distance FL from the lens surface, provided the lens hassufficient aperture size and its profile shape is properly defined withrespect to the refractive indexes of the lens material and host medium.The operational principle of the refractive dielectric lenses is basedon Snell's law, which predicts the tilt (refraction) of optical rays atthe air-dielectric boundary of the lens due to the different phasevelocity in the two media. To enable the desired focusing function, thelens must have an aperture size of at least a few wavelengths in thehost medium, with a typical physical size varying from a few microns incase of microlenses to several centimeters in case of camera objectivelenses. Their resolution is limited by the Abbe diffraction limit and istypically larger than one wavelength in the host media.

There also exist Fresnel-type diffractive lenses, whose operationalprinciples rely on the interference of the waves diffracted by multipleconcentric rings, as illustrated by FIG. 1B. If compared to refractivelenses of FIG. 1A, such lenses have smaller thickness, however, theyusually suffer from strong chromatic aberrations. Their resolution islimited by the diffraction limit, like refractive lenses.

As already mentioned above, the spatial resolution of far-field focusingsystems (e.g. refractive and diffractive lenses) is limited by the Abbediffraction limit set by ˜λ/2n sin α, where λ is the vacuum wavelength,n is the host media refractive index, and α is the half aperture angleof the lens (by far-field focusing systems, it is meant here systemswhich create focal spots FS at distances larger than a few wavelengths,i.e. in the far zone). Thus, a higher resolution can be achieved eitherby increasing the lens aperture size or by reducing the focusingdistance FL. The latter explains the growing interest in near-fieldfocusing systems, which create focal spots FS in the near zone. Thisinterest is also strongly supported by the growing number ofapplications across different domains, which require near-field lightprocessing with the highest possible resolution, such as for example inmicroscopy, spectroscopy or metrology.

At present, there are several near-field focusing techniques available,based on subwavelength aperture probes (L. Novotny et al., “Near-fieldoptical microscopy and spectroscopy with pointed probes”, Annu. Rev.Phys. Chem. Vol. 57, pp. 303-331, 2006), planar subwavelength-patternedstructures (U.S. Pat. No. 8,003,965), and photonic nanojet microspheredielectric lenses. The latter solution (i.e. nanojet microspheres), asdescribed for example in U.S. Pat. No. 7,394,535, and illustrated inFIG. 1C, is often referred to as the most effective one becausemicrospheres can simultaneously provide the subwavelength resolution anda high level of field intensity enhancement (FIE). As shown on FIG. 1C,they allow generating a nanojet beam NB. This photonic nanojet is anoptical intensity pattern induced at a shadow-side surface of adielectric microsphere. Patent document US 2013/0308127 also describesnanojet devices, allowing to enhance Raman emissions from a sample byusing a microsphere to confine the impinging radiation into a photonicnanojet and thereby increase the intensity of the radiation that isstriking the sample. The amount of enhancement may be improved byconfiguring the diameter and refractive index of the microspheres inconjunction with the dispersion and the wavelength of the radiation toincrease the intensity of the beam of radiation in the photonic nanojet.

Despite their attractive performance characteristics, the use ofmicrospheres is associated with certain difficulties related to their(i) precise positioning, (ii) integration with other optical components,and (iii) non-compatibility with the established planar fabricationtechniques. These difficulties affect feasibility and increase thefabrication and assembly costs of the nanojet based devices.Potentially, the assembly problem can be solved using nanoscalepatterned structures or hollow tubing, but these solutions may not becompatible with some applications.

An alternative solution for nanojet microsphere lenses was proposedrecently based on the solid dielectric cuboids (SDC). As demonstrated byV. Pacheco-Pena et al. in “Terajets produced by dielectric cuboids”,Applied Phys. Lett. Vol. 105, 084102, 2014, and illustrated by FIG. 1D,when illuminated by a plane wave, the SDC lenses can also producecondensed beams TB, similar to the nanojet beams observed formicrospheres, with subwavelength dimensions, provided the size and shapeof cuboids is properly adjusted with respect to the incident wavelengthand the refractive index of the cuboid material. The best spatialresolution (˜λ/2, where λ is the wavelength in the host medium) andfield intensity enhancement (factor of ^(˜)10) is achieved for SDC withdimensions of about one wavelength in the host medium and the refractiveindex ratio n₂/n₁˜1.5, where n₁ and n₂ are refractive indexes of thehost medium and cuboid material, respectively.

Although the rectangular shape of SDC lenses can be advantageous forsome planar fabrication methods (e.g. micromachining or lithography),the fabrication of SDC lenses operating in the optical range can bedifficult or even impossible because of the following constraints:

-   -   Strict requirements imposed on the cuboid size and shape,    -   Absence of materials with the desired refractive indexes (in the        optical range, the refractive index of common optical glass and        plastics, which can be used as a host medium, varies from n₁≈1.3        up to 2.0, whereas, according to V. Pacheco-Pena et al, the        desired value of the cuboid lens refractive index should be n₂        ^(˜)2.25 (suggested ratio n₁/n₂=1.5 with n₁≈1.5 for a standard        glass) that is out of range for standard optical materials.    -   No solution provided for setting the position of such lenses in        space is provided.

Last, it is worth mentioning one more alternative solution for thenear-field enhancement available in the optical range. This solution isbased on the phenomenon known as surface plasmon polaritons (SPP). TheSPP phenomenon enables one to create subwavelength hot spots with a veryhigh field intensity. In particular, SPP-based components findapplication in color filtering and display technologies, as described byY. Gu et al. in “Plasmonic structures color generation via subwavelengthplasmonic nanostructures”, J. Nanoscale, vol. 7, pp. 6409-6419, 2015.However, the SPP fields are tightly coupled to the metal and decayexponentially away from the surface, which prevents the use of SPPdevices for the optical systems requiring a ‘long-range communication’or far-field beam forming. Moreover, the SPP can only be excited underspecific conditions that include:

-   -   certain material properties of the metals (i.e. negative real        part of the relative permittivity that is only intrinsic to some        noble metals in the visible light spectrum),    -   normal E-field component in the incident field,    -   use of a SPP launcher (e.g. dielectric prism or grating).

These constraints are not always acceptable.

All prior art focusing methods and components thus suffer from certainlimitations and do not fully satisfy the needs of the today and futuremicro and nanotechnologies. Some limitations, intrinsic to all (or atleast some) of the available focusing devices, are associated with:

-   -   the physical dimensions of the components,    -   a limited spatial resolution,    -   a limited choice of dielectric materials (limited refractive        index variation range),    -   some fabrication/integration difficulties,    -   certain limitations in the performance characteristics of the        devices (e.g. chromatic aberrations and/or polarization        sensitive response) linked to their operational principles.

It would hence be desirable to provide a new technique for forming fieldintensity patterns in the near zone from electromagnetic waves, andnotably for generating condensed low-dispersive beams of radiation inthe near zone, which would not present at least some of these drawbacks.

3. SUMMARY

In one aspect, a device for forming a field intensity distribution inthe near zone, from electromagnetic waves which are incident on saiddevice, is disclosed. Such a device comprises at least one layer ofdielectric material; a surface of said at least one layer of dielectricmaterial has at least one abrupt change of level forming a step, and atleast a lower and lateral part of said surface with respect to said stepis in contact with a substance having a refractive index lower than thatof said dielectric material.

The present disclosure thus provides a new generation of components,allowing to form desired field intensity distribution in the near zone,with the aid of purely dielectric microstructures. Such devices maynotably be used for focusing electromagnetic waves, and for generatingcondensed low-dispersive optical beams (so-called nanojets) in the nearzone from a plane electromagnetic wave incident on the device (notably,but not exclusively, from the bottom part of the dielectric layer, whichsurface can be even). When used in a reverse mode, they may also be usedfor correcting a non-planar wave front of an electromagnetic wavegenerated by a source of electromagnetic radiation or by anotherbeam-forming element, located close to the top part of the dielectriclayer, which surface has an abrupt change of level. In particular, sucha correction can include transformation of a non-planar wave front(typical for beams and spherical waves) into a locally planar wave frontor beam, or another shaped wavefront.

In other words, when used at optical wavelengths, such a device mayproduce at least one condensed optical beam in the near zone (i.e. ananojet beam), thus creating at least one high-intensity focal spot inan imaging plane, which is defined in the near zone of the device. Theuse of such a device is of course not limited to such wavelengths.

As will be described in greater detail in the following part of thepresent disclosure, such spots have shapes, which are typically circularor oval, more or less elongated. The shape of the spots is defined hereby the shape of a contour line surrounding the area with field intensityequal to half of the maximum intensity in the corresponding hot spot.Spots may also have a more complex shape if more than one concavesegment of the step contributed in the formation of a single spot. Theirsmallest size is circa half of the wavelength in diameter, when definedat half power, which is close to the Abbe diffraction limit.

When a pattern of several spots is formed, the spacing between the spotsshould be of at least one wavelength, otherwise two spots could mergeforming a common hot spot of complex shape.

The field intensity enhancement (compared to a plane wave propagating inthe same host medium) associated to such spots varies from a factor oftwo, for a step with a straight boundary, to a factor of ten, or even upto twenty for more complex shapes of steps.

The abrupt change of level in the surface induces a step of index for anincident electromagnetic wave, which reaches the device in the vicinityof the step in the dielectric layer. Such a step of index gives birth toa complex electromagnetic phenomenon, which will be described in greaterdetail in relations to the figures in the foregoing disclosure. Such acomplex electromagnetic phenomenon, which involves diffraction of theincident wave on the lower part of the edge with respect to the step,coupled to refraction of the diffracted wave on the lateral part of thestep allows producing condensed beams and thus different field patternsin an imaging plane located in the near zone, depending on the featuresof the step, and on the difference of refractive indexes between thedielectric material and the substance covering its lower and lateralsurfaces. The apparition of the nanojet beam results from theinterference of diffracted/refracted wave and the incident plane wave.

The substance in contact with the lower and lateral surfaces of the stepmay simply be air, another gas, vacuum, a liquid or any other materialwith a refractive index lower than that of the dielectric material. Itmust also be noted that the lateral part of the step need notnecessarily be vertical, and may show an angle with respect to thenormal to the surface of the dielectric layer. Moreover, it may notnecessarily be a straight-line segment.

There is no restriction on the bottom surface of the dielectric layer,which may be plane, or not. The dielectric layer may notably beflexible.

Such a device according to embodiments of the present disclosure thusallows generating low-dispersive beam(s) in the near zone. Such afunction may be controlled by appropriately choosing an appropriaterefractive index ratio for the materials of the dielectric layer and thesubstance/element, the step's edge line length and curvature, as well asits base angle, as will become more apparent while reading thefollowing.

According to an embodiment of the present disclosure, said step isformed by an edge of at least one cavity made in said at least one layerof dielectric material.

Hence, as compared to a single step in the layer of dielectric material,all the edges of the cavity may contribute to generating a fieldintensity distribution in the near zone, notably producing (i.e. givingrise to) at least one condensed beam of radiation. Depending on theshape of the cavity cross-section, it is possible to produce differentfield patterns obtained from a combination of the beams generated by thecavities.

According to another embodiment, said at least one cavity is athrough-hole in said at least one layer of dielectric material. Theheight of the cavity(ies) thus corresponds to the thickness of thedielectric layer. In case the cavity is not a through-hole, its heightis hence smaller than the thickness of the dielectric layer; it may belocated at any position with respect to the top and bottom surfaces ofthe dielectric layer. The cavities need not be all the same ones.

According to another embodiment, said at least one cavity belongs to atleast one set of at least two cavities.

Cavities may be arranged into arrays of cavities, or non-regulararrangements forming a peculiar pattern, in order to generate specificfocused beams in the near zone, or an array of beams, which may be ofinterest for some applications, like optical sensors. An array of two ormore closely positioned cavities can be used in order to provide controlover the field distribution in a larger area and/or to increase fieldintensity at some selected point(s). Moreover, the arrays of cavitiesmay be planar (with all base faces of all cavities laying in the sameplane) or not, and can be made of identical cavities or not.

According to yet another embodiment, said at least one cavity istargeted to be cylindrical or cone-shaped.

By cylindrical cavity, it is meant here, and throughout this document, acavity is a shape is a generalized cylinder, i.e. a surface created byprojecting a closed two-dimensional curve along an axis intersecting theplane of the curve. In other words, such a cylinder is not limited to aright circular cylinder but covers any type of cylinder, notably, butnot exclusively, a cuboid or a prism for example. The cavity may alsohave the form of a cone. Its main axis may be orthogonal to the surfaceof the bottom of the cavity, or be tilted. Due to the fabricationtolerances, the cavities may also have imperfect shapes, and it must beunderstood, for example, that cavities targeted to be shaped ascylinders, may become cone-shaped cavities with S-shape cross-sectionsduring the manufacturing process.

More generally, such cavities are formed as cylinders or cones with anarbitrary cross-section, which can be adapted (optimized) in order toproduce a desired near-field pattern, i.e. a desired field intensitydistribution in the xy-plane (typically orthogonal to the incident wavepropagation direction). This pattern may have one or multiple hot spotswith identical (or different) field intensity level.

Non-symmetric cavities are also possible. For example, a cavity whichcross-section in the xy-plane is triangular will create three spots. Oneof them can be enhanced if the corresponding face is concave, as will beexplained in greater detail in relation to the figures.

According to an embodiment, a height H of said step, or of said cavity,is targeted to be such that

${H > \frac{\lambda_{1}}{2}},$

where λ₁ is a wavelength of said electromagnetic waves in saiddielectric material. Actually, the nanojet phenomenon is well pronouncedfor a cavity height varying from about half to a few wavelengths in thehost medium (dielectric material). A minimum height is needed to form alocally planar wave front, which will give rise to the nanojet beam.

Moreover, the nanojet beam appears at the bottom of the cavity. As inmost applications it is desired to have a beam, which extends beyond theheight of the cavity, the height of the cavity should be smaller thanthe length of the generated nanojet beam, which is generally about twoto five (in some cases ten or even more) wavelengths.

According to an embodiment, such a device also comprises at least onelayer forming a substrate abutting said layer of dielectric material.

Such a substrate may contribute to the mechanical rigidity of thedevice.

According to a further embodiment, such a device also comprises at leastone layer forming a superstrate, said at least one layer of dielectricmaterial being located between said substrate and said superstrate.

Hence, the device may take the form of a planar optically-transparentelement, comprising two glass or plastic plates (namely the substrateand the superstrate), between which a dielectric material with void orfilled hollow microcavities is embedded. The superstrate may of coursebe non-planar, and follow the shape of the substrate for example.Actually, the pattern of the field intensity distribution generated bythe device when illuminated by a plane wave incident normal to the basesolely depends on the cavity base angle (or step angle), on the cavitycross-section shape, and on the index ratio between the dielectricmaterial and the substance filling the cavity (or covering the lowerpart of the surface with respect to the step).

It must be noted that the radiation of the beams will change for inclineincidence of the plane wave, with a shape of the beam well preserved forthe incident angles of about +/−30°, depending on the index ratio, thesize, base angle and curvature of the cavity edge line.

According to an embodiment, the substrate and the superstrate are madeof the same dielectric material as said at least one layer of dielectricmaterial.

According to an embodiment, said dielectric material belongs to thegroup comprising:

-   -   glass;    -   plastic;    -   a polymer material, such as PMMA (Poly(methyl methacrylate)) or        PDMS (Polydimethylsiloxane). It must be noted that air is not        considered as a candidate dielectric material for the device        according to the present disclosure.

Such a device can hence be fabricated using standard dielectricmaterials, which are easy to find and inexpensive.

According to an embodiment, a material of said superstrate belongs tothe group comprising:

-   -   glass;    -   plastic;    -   a polymer material.

In one embodiment of the disclosure, it is proposed a device for forminga field intensity distribution in the near zone, from propagatingelectromagnetic waves which are incident on said device. Such devicecomprises:

at least one layer of dielectric material, having a first refractiveindex n₁ with a surface having at least one abrupt change of levelforming a step;

an element having a second refractive index n₂ lower than said firstrefractive index n₁, which is in contact with said step; and

said step generates a beam which is tilted compared to a propagationdirection of said electromagnetic waves.

In a variant, the titled beam has a length that can vary from ½λ₁ toseveral wavelengths, with λ₁ being a wavelength of said electromagneticwaves in said dielectric material.

In a variant, the device comprises a receiving element positioned alonga propagation direction of said titled beam.

In a variant, the receiving element is positioned at a hot spot of saidbeam.

In a variant, the receiving element is positioned at a distance d fromsaid step, where d is between one λ₁ to 10λ₁, with λ₁ being a wavelengthof said electromagnetic waves in said dielectric material.

In a variant, the titled beam is associated with an angle of radiationwhich is defined as a function of said first refractive index n₁ and/orsaid second refractive index n₂, and/or incident angles of said incidentelectromagnetic waves compared to said step, and/or a step base angle.

In a variant, the angle of radiation is around a value equal to (90°−asin(n₂/n₁))/2.

In a variant, the angle of radiation is around 23° when n₁=1.49 andn₂=1, and around 30°, when n₁=2 and n₂=1.

In a variant, the device is adapted to form beams for incidentelectromagnetic waves that are monochromatic electromagnetic waves, eachof said monochromatic electromagnetic waves having a wavelength equal toa value which is around 480 nm or 525 nm or 650 nm.

4. BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure can be better understood with reference to thefollowing description and drawings, given by way of example and notlimiting the scope of protection, and in which:

FIGS. 1A to 1D depict prior art conventional refractive (FIG. 1A) anddiffractive (FIG. 1B) lenses, nanojet miscrosphere (FIG. 1C) and terajetcuboids (FIG. 1D);

FIG. 2 is a schematic drawing of a nanojet beam produced by a dielectriclayer with a step according to an embodiment of the present disclosure,with FIG. 2A a side view and FIGS. 2B and 2C top views according to twoalternate embodiments;

FIG. 3 illustrates an alternate embodiment to FIG. 2A, in which the stephas a rounded top edge;

FIG. 4 illustrates the topology of a microcavity formed in a layer ofdielectric material according to an embodiment of the presentdisclosure;

FIGS. 5a to 5e illustrate the formation of a nanojet beam by the cavityof FIG. 4 having a circular cylinder shape when illuminated by a planewave from below at different wavelengths;

FIGS. 6a and 6b provide an analysis of the nanojet beam radiation angleof FIGS. 5a to 5 e;

FIGS. 7a and 7b illustrate the complex electromagnetic phenomenaunderlying embodiments of the present disclosure;

FIGS. 8a to 8c illustrate near-field maps of nanojet beam produced bycircular cylindrical cavities of different heights when illuminated by aunit-amplitude plane wave from below according to embodiments of thepresent disclosure;

FIGS. 9a to 9d show nanojet beams produced by a hollow circularcylindrical cavity under different angles of incidence of theunit-amplitude plane wave in XZ-plane (top row) and a section in XYplane (bottom row);

FIGS. 10a and 10b illustrate the nanojet beams phenomenon as observedfor different host media with different refractive indices in XZ-plane(top row) and a section in XY plane (bottom row) according toembodiments of the present disclosure;

FIG. 11 shows the top view of four exemplary cylindrical cavities havingeach a different shape of the cross-section boundary, namely: (a)circular, (b) square, (c) 8-shape, and (d) rectangular, according toembodiments of the present disclosure;

FIGS. 12a to 12d show the corresponding simulated near-field maps foreach cavity of FIG. 11 in XZ-plane (top row) and a section in XY plane(bottom row);

FIGS. 13a to 13c are schematic drawings of the field intensitydistribution in the imaging plane for three exemplary cylindricalcavities with different cross-sections;

FIG. 14 provides a schematic drawing for the implementation of acomponent according to an embodiment of the present disclosure;

FIGS. 15a to 15f illustrate side views of alternate embodiments to thecomponent of FIG. 14;

FIG. 16 illustrates a typical use scenario of the devices of FIGS. 14and 15;

FIG. 17 illustrates a specific embodiment of the present disclosure,according to which the focusing component is based on a 2×2 planar arrayof identical hollow cuboid-shaped cavities embedded in a host medium;

FIG. 18 illustrates an alternate embodiment, in which the hollowcuboid-shaped cavities of FIG. 17 are replaced with hollow circularcylinders, oriented along the plane wave propagation direction;

FIG. 19 illustrates yet another embodiment, in which a 2×2 array ofhollow circular cylinders is created at the boundary of the dielectricmedium and free space;

FIG. 20 illustrates the profiles of the nanojet beams produced by allthree embodiments of FIGS. 17, 18 and 19;

FIG. 21 provides two additional exemplary embodiments based onsingle-periodic (FIG. 21a ) and double-periodic (FIG. 21b ) arrays ofhollow cylinders embedded in a host medium;

FIGS. 22a and 22b are schematic drawings illustrating a possibleimplementation embodiment for the periodic structures of FIGS. 21a and21b with side views on the top row and top views on the bottom row;

FIG. 23 presents an alternate possible implementation embodiment for theperiodic structures of FIGS. 21a and 21 b.

The components in the figures are not necessarily to scale, emphasisinstead being placed upon illustrating the principles of the invention.

5. DETAILED DESCRIPTION

The general principle of the present disclosure relies on the design ofa new dielectric microstructure, which may be used for generatingcondensed low-dispersive optical beams in the near zone, also callednanojets. Its use is not limited to optical wavelengths. A step ofrefractive index in the dielectric microstructure gives rise to adiffraction phenomenon, which is in turn coupled to refraction andinterference phenomena, and allows generating condensed beam(s) ofradiation in the near zone when the dielectric microstructure isilluminated by a plane wave, depending on the shape and dimensions ofthe structure.

To the reverse, such a dielectric microstructure may be used forconverting a non-planar wave front of an electromagnetic wave generatedby a local source of electromagnetic radiation or by anotherbeam-forming element, located close to the lateral edge of the step,into a locally planar wave front or beam.

The formation of one or several nanojet beam(s) in the near zone appearswith a plane (or locally plane) wave incident on the device. When thedevice functions in reverse mode, with a local source placed in thefocal point (i.e. in the nanojet beam region), a locally-plane wave isformed that is equivalent to a infinitely-long beam extending to theinfinity.

The beam-forming function of such nanojet devices may be controlled bysetting the step's edge line length and curvature, as well as its baseangle.

Such a general principle allows designing new focusing and beam-formingcomponents, which can replace the conventional focusing devices in denseoptic and photonic systems, like integrated optical sensors used inphoto/video cameras that are essential components in the field of mobiletechnology (e.g. smartphones, tablets, Augmented Reality (AR) andVirtual Reality (VR) glasses).

Thanks to the ultra-compact dimensions of such dielectricmicrostructures, as well as to the wide range and diversity of fieldpatterns, which can be produced through the use of such microstructures,the present disclosure can be used in several fields of technology,including, but not limited to:

-   -   eyewear electronics, including AR and VR glasses;    -   optical sensors for photo/video/light field cameras;    -   light communication systems, including quantum computers;    -   bio/chemical sensors, including lab-on-chip sensors;    -   microscopy, spectroscopy and metrology systems;    -   integrated lens antennas for applications in the        millimeter/sub-millimeter/infrared (IR) wavelength ranges.

The following discussion mostly focuses on optical applications and thusrefers to material properties and fabrication methods relevant tonanoscale structures and wavelength. Nevertheless, the proposed designconcepts can be easily scaled to other wavelength ranges, includingmicrowaves, mm-waves, THz, IR, visible light and UV.

Inventors of the present disclosure have reached the conclusion thatdiffraction of a plane electromagnetic wave on the base surface of adielectric material in the close vicinity of an abrupt change of levelof this surface, also called a step, can result in the formation ofcondensed optical beams (so-called nanojets), when the surface on whichdiffraction occurs is in contact with a substance (material or gas)having a lower refractive index than that of the dielectric material.The number of beams and shape of each individual beam can be controlledby the variation of the step size and shape of the step edge lineadjacent to the lateral and lower surfaces of the step. Unlike thewell-known diffracted beams predicted by the Fresnel theory, the nanojetbeams are low-dispersive (they show no or small wavelength dependence).Moreover, a same nanojet focusing component according to the presentdisclosure can produce multiple independent beams (having identical ornon-identical shape) associated with different segments of the step edgeline, which is not possible with Fresnel diffractive lenses. Theseunique features make the nanojet-based focusing components according tothe present disclosure attractive for many today and futureapplications.

FIGS. 2 to 10 allow understanding the physical phenomena explaining theformation of nanojet beams according to the present disclosure.

FIG. 2 illustrates an embodiment of the present disclosure, where anabrupt change occurs in the level of the surface of a dielectric layer112, thus forming a step in the layer. FIG. 2a shows a side view of thedielectric layer 112. FIGS. 2b and 2c respectively show top views incase of a step with a straight (FIG. 2b ) and curved (FIG. 2c ) edgelines.

As shown in FIG. 2a , the device is illuminated by an incident wave 20,coming from the base of the device and orthogonal to the base surface ofthe dielectric layer 112, along the z-axis. As schematically shown bythe dashed arrows in FIGS. 2b and 2c , a nanojet beam 55 originates fromthe base edge of the step, which comprises a horizontal part 120 and alateral part 121 (which may also be tilted with respect to the z-axis).

Spots referenced 22 to 24 indicate the corresponding hot spots in thenear-field distribution formed in the imaging plane. The specific fielddistribution with two hot spots 23, 24 observed in FIG. 2c is associatedwith the shape of the edge line with two concave segments responsiblefor the formation of two independent nanojet beams.

FIG. 3 illustrates an alternate embodiment to FIG. 2a , in which thestep formed in the dielectric layer 112 shows a rounded top edge 122.Such a step will also generate a nanojet beam 55, which originates fromthe base edge of the step, when illuminated by an incident wave 20, likein FIG. 2 a.

FIG. 4 illustrates an embodiment of the present disclosure, according towhich the step formed at the surface of a layer of dielectric materialis in fact the edge of a microcavity 111 made in the layer of dielectricmaterial 112. The present disclosure is of course not limited to such anembodiment, and any abrupt change of level and index close to thesurface of the dielectric material is sufficient for generating thephysical phenomena, which will be described hereafter. Such a step canindeed be considered as the edge of a cavity of infinite size.

It must be understood that, in case of a step, the focusing function isto be associated not with the entire structure, but with an elementarysegment of this step discontinuity. The other segments of the stepdiscontinuity will contribute to the formation of other nanojet beamsthat may form all together (i) a wide uniform “blade like” nanojet beamas in case of an line of steps (see FIGS. 2a and 2b ), or (ii) a ring incase of an arbitrary-large circular cylindrical cavity (see FIGS. 12a,13a ), or (iii) an arbitrary number of localized beams of differentshapes produced by a curvilinear edge of an arbitrary-shaped cavity (seeFIG. 13c ).

For sake of simplicity, we therefore focus hereafter on the example of amicrocavity 111 formed in the layer of dielectric material 112, like theone illustrated in FIG. 4.

As may be observed, such a cavity is cylindrical, with a cross-sectionof arbitrary shape. By cylindrical cavity, it is meant here, andthroughout this document, a cavity which shape is a cylinder, i.e. asurface created by projecting a closed two-dimensional curve along anaxis intersecting the plane of the curve. In other words, such acylinder is not limited to a right circular cylinder but covers any typeof cylinder, notably, but not exclusively, a cuboid or a prism forexample.

FIG. 4 gives some notations, which will be used hereafter in thedocument. As may be observed, the cavity is immersed in a host mediumMedia 1 112 of refractive index n₁, and is void or filled with amaterial (air, gas, liquid, polymer material . . . ) Media 2 ofrefractive index n₂, such that n₂<n₁.

For example, the cavity has a form of a circular cylinder filled in withvacuum (n₂≅1) and embedded in a homogeneous non-dispersive dielectricmedium with an example refractive index n₁=1.49.

A plane wave is incident from below along z-axis (see FIG. 4 fornotations). FIG. 5 illustrates the formation of a nanojet beam by such acavity when illuminated by this plane wave. More precisely, FIGS. 5a to5e each correspond to a different wavelength of the incidentelectromagnetic wave, namely λ₀=450, 500, 550, 600 and 650 nm, and shownear-field maps in the XZ-plane plotted in terms of the time averagePoynting vector for the case of a hollow circular cylinder (n₂≅1,L_(z)=740 nm, R=370 nm) embedded in a medium with refractive indexn₁=1.49. The cavity is illuminated by a unit-amplitude E_(y)-polarizedplane wave from below.

As may be observed, the shape of the nanojet beam and its directionremain stable in a wide wavelength range for low dispersive dielectricmaterial (n₂/n₁ close to constant when wavelength varies). The detailedanalysis of the nanojet beam radiation angle is reported in FIGS. 6a and6b . FIG. 6a illustrates the Poynting vector in the XZ-plane at threedifferent planes defined as z=z₀−L_(z), for the five differentwavelengths of FIG. 5. FIG. 6b illustrates the nanojet beam radiationangle calculated based on the positions of maxima in FIG. 6a as afunction of wavelength.

These data extracted from near-field maps reveal that the variation ofthe nanojet beam radiation angle does not exceed 3° for the wavelengthrange from at least 450 to 750 nm (hereafter the dielectric material isassumed to be homogeneous, isotropic and non-dispersive). As it is seenin FIG. 6a , the major contribution to the angle variation comes fromthe beam tilt above the cylinder (z₀=1500 nm, where z₀ is a relativeposition of the imaging plane defined with respect to the cavity base120, i.e. z₀=z−L_(z)), whereas the beam shape at (z₀=500 nm) remainsstable for the entire wavelength range. Such a behavior is not typicalfor Fresnel-type diffractive lenses and thus requires detailedexplanations.

The origins of the nanojet beams can be explained by the combination ofthree electromagnetic phenomena, which occur in the vicinity of the baseedge of the hollow cavity (or more generally in the vicinity of theabrupt change of level in the surface of the dielectric material),namely:

-   -   diffraction from the index-step discontinuity associated with        the base 120 of the cavity (or, more generally with the surface        of lower level of a step formed in the host medium),    -   refraction of the diffracted wave at the lateral edge 121 of the        cavity (or more generally on the lateral part of the step), and    -   interference of the refracted wave and the incident plane wave        outside the cavity (or more generally in the host medium).

A schematic drawing illustrating these three phenomena is given in FIGS.7a and 7b . As in FIGS. 5 and 6, we assume that host media is anoptically-transparent non-dispersive dielectric material with arefractive index n₁=1.49 (e.g. plastic or glass) and the cavity isfilled with vacuum, n₂=1. The incident plane wave arrives from below inthe diagrams.

The key elements of the complex electromagnetic phenomena illustrated inFIGS. 7a and 7b are the following:

-   -   The incident plane wave induces currents at the dielectric-air        boundary 120 associated with the cavity base (or more generally        when reaching the step of index in the host medium induced by        the abrupt change of level in its surface);    -   These induced currents are considered as Huygens secondary        sources 50 to 53;    -   In line with the diffraction theory, the spherical waves 54        radiated by the Huygens sources cause some power leakage towards        the ‘shadow region’, i.e. towards the lateral boundary 121 of        the cavity;    -   While crossing the lateral (vertical) boundary, the waves        radiated by the Huygens sources experience refraction that        causes a tilt of the refracted wave on a certain angle in        accordance with the Snell-Descartes's law.    -   In FIG. 7b , we can notice that outside the cavity the wave        fronts coincide for different Huygens source positions along the        cavity base line, thus creating a local field enhancement. The        planar shape of these fronts evidences for the creation of a        directive beam propagating out of the cavity.    -   Finally, outside the cavity the refracted wave is constructively        interfering 56, 57 with the plane wave incident from below        giving rise to the nanojet beam 55.

The nanojet beam creation is hence explained by phenomena that arenon-dispersive in nature, namely (i) edge diffraction, (ii) refractionof the wave at the interface of two dielectric media, and (iii)interference. This explains why the shape of the beam and its radiationangle remain stable versus wavelength, as may be observed in FIGS. 5a to5 e.

Moreover, for the case of a normal incidence of a plane wave on the baseof the cavity, the nanojet beam radiation angle is defined by theSnell's law and, thus, is only a function of two parameters:

(i) ratio between the refraction indexes of the host media and cavitymaterials, and(ii) the base angle of the prismatic cavity. For sake of simplicity, inthe foregoing, we only consider a prismatic cavity with the base angleequal 90° thus having a cylindrical shape with vertical edges.

Last, the nanojet beam-forming phenomenon is associated with the edge(not a full aperture) of the cavity and occurs in the 2-D vertical planeorthogonal to the cavity cross-section (see FIG. 4 for notations).

As follows from FIG. 7b , the main contribution to the formation of theplanar wave front of the refracted wave outside the cavity comes fromthe Huygens sources 50-53 located close to the lateral edge 121 of thecavity. Because of this, the refraction angle of the wave radiatedoutward the cavity is close to the critical angle for the wave incidenton the same boundary from outside (FIG. 7a ):

θ₁≈θ_(TIR), where θ_(TIR)=sin⁻¹(n ₂ /n ₁) is the critical angle.  (1)

The nanojet beam 55 is finally created as a result of the interferencebetween the refracted wave and the plane wave incident from below, theangle of radiation of the nanojet beam (θ_(B)) is defined by a vectorsum of the two waves as schematically shown in FIG. 7a . Theseconsiderations lead one to the following approximate formula for theradiation angle of the nanojet beam:

θ_(B)≈(90°−θ_(TIR))/2  (2)

According to Eqn. (2), in the case of a host medium with index n₁=1.49(θ_(TIR)=41.8°), the nanojet beam radiation angle should be θ_(B)^(˜)24° that is slightly larger than observed in the full-wavesimulations (see FIG. 6b ). This difference is explained by someassumption made in the qualitative analysis. First, this analysis doesnot take into account the difference in the amplitude of the refractedand incident waves. Second, it does not take into account the rayslaunched by the Huygens sources located close to the cavity edge fromoutside that experience the total internal reflection on the cavitylateral edge. Being totally reflected, these rays also contribute to theformation of the nanojet beam. Note that these two effects are relatedto the total internal reflection phenomenon and thus cannot beaccurately characterized using Snell/Fresnel model. Nevertheless, botheffects (i) depend on the ratio of refraction indexes of the two mediaand (ii) result in reducing the nanojet radiation angle. Thus, theactual nanojet radiation angle can be smaller than that predicted byEqn. (2).

FIGS. 8a to 8c illustrate near-field maps of the nanojet beam producedby cylindrical cavities (n₁=1.49, n₂=1, R=370 nm) of different heights((a) H=L_(z)=370 nm, (b) H=L_(z)=740 nm, (c) H=L_(z)=1110 nm) whenilluminated by a unit-amplitude plane wave from below. As may beobserved, the nanojet phenomenon is well pronounced for the cavity sizevarying from about one to a few wavelengths in the host medium, namely½λ₁<L_(z)<3λ₁.

The minimum height is needed to form the planar wave front illustratedin FIG. 7b that gives rise to the nanojet beam. However, the height ofthe cavity (or the height of the step) should not be too large ascompared to the length of the nanojet beam, in order for it to be usefuloutside the focusing component.

As shown on FIGS. 8a to 8c , the length of the nanojet beam can varyfrom a few to several wavelengths in the host medium depending on thecavity shape and size.

Based on the 2-D ray-tracing analysis of FIG. 7b , the main contributionin the formation of the nanojet beam comes from the feeds located closeto the cavity lateral edge (or to the lateral part of the step). Thecorresponding ‘effective aperture’ responsible for the formation of thenanojet beam is estimated as about one half of the wavelength in themedium inside the cavity (½λ₂) that is to be counted from the lateraledge inward the cavity. For the cavity having arbitrary shape, thisaperture is to be defined along the line orthogonal to the cavitycross-section boundary, S (see FIG. 4).

In 2-D case (which may correspond to any vertical cross-section, e.g. inxz-plane), the local field intensity enhancement (FIE) achieved thanksto the nanojet beam formation is about a factor of 2 compared to theincident plane wave. A larger FIE can be achieved by modifying the shapeof the cavity cross-section, S, as will be explained hereafter ingreater details, or by combining contributions from several cavities.

The nanojet beam full width at half power (FWHP) can vary from about ½λ₁ (i.e. the Abbe diffraction limit) to several wavelengths and moredepending on the shape of the cavity.

FIGS. 9a to 9d show nanojet beams produced by a hollow cylindricalcavity (n₁=1.49, n₂=1, L_(z)=740 nm, R=370 nm) under different angles ofincidence of the unit-amplitude plane wave in XZ-plane, namely θ=0° inFIG. 9 a, θ=10° in FIG. 9 b, θ=20° in FIG. 9c and θ=30° in FIG. 9 d.

The symmetry of the near-field patterns in the XY-plane (see FIG. 9a )evidences that the beam shape and radiation angle remain nearly constantfor both TE (Transverse Electric) and TM (Transverse Magnetic)polarizations of the incident wave.

Moreover, in case of an inclined incidence, it may be observed in FIG. 9that the beam radiation angle changes in correspondence to the angle ofincidence of the plane wave. The shape of the beam and field intensityenhancement remain nearly constant for incidence angle up to aboutθ_(B).

FIG. 10 illustrates the nanojet beams phenomenon as observed fordifferent host media, including standard optical plastics and standardor doped glass. Such nanojet beams are produced by a hollow circularcylindrical cavity having the same physical dimensions (n₂=1, L_(z)=740nm, R=370 nm) but embedded in a host medium of refractive index n₁=1.49,in FIG. 10a and n ₁=2.0, in FIG. 10 b.

The understanding of the complex electromagnetic phenomena illustratedthrough FIGS. 2 to 10 allows designing interesting devices, which can beused as nanojet focusing components, beam-forming components, or moregenerally components for forming desired field intensity distribution inthe near zone. Such components may be used for transforming an incidentplane wave into one or multiple independent beams, or, conversely, fortransforming an incident non-planar wave (whatever its wavelength) intoa locally plane wave, in accordance with the symmetrical path propertiesof electromagnetic waves.

As explained above in the present disclosure, the formation of thenanojet beams is associated with the lateral part of the step in thelayer of dielectric material, or with the edge of the cavity, but notits full aperture. By optimizing the shape of the cross-section of thecavity S, it is possible to control the shape of the nanojet beam(s)produced by this cavity.

FIG. 11 shows four exemplary cylindrical cavities having each adifferent shape of the cross-section boundary, namely: (a) circular, (b)square, (c) 8-shape, and (d) rectangular. The dashed lines schematicallyshow some vertical cut planes in which the nanojet beams are generatedwhen these cavities are illuminated by a plane wave propagating alongthe z-axis, from the plane of the figures. These cut planes are definedwith respect to the direction of the normal vectors defined at thecorresponding points of the cavity cross-section boundary. Thecorresponding simulated near-field maps for each cavity are shown inFIGS. 12a to 12d , which illustrate the near-field patterns in xz-plane(y=0) and xy-plane (z=1000 nm−z₀) for hollow cavities (L_(z)=L_(x)=R=740nm) having same height and radius but different cross-section shapesilluminated by a unit-amplitude plane wave from below: (a) circular, (b)square, (c) 8-shape, (d) rectangular. The spots 101 to 104 in thexy-plane identify the nanojet beams, whose shapes and positions are wellin line with the predictions given in FIG. 8 (these near-field maps arecomputed at arbitrary-selected xy-plane z₀=1000 nm).

In particular, FIG. 12a shows that the axially-symmetrical circularcavity produces a diverging conical beam. It is interesting to note thatthis conical beam is nearly-symmetrical (see the near-field pattern inhorizontal xy-plane), which is an evidence for thepolarization-insensitive behavior of such component. In thisconfiguration, the maximum FIE is equal to a factor of ^(˜)2, comparedto the plane wave propagating in the same host media.

Note that the near-field maps in FIG. 12 are plotted in terms of thetime average Poynting vector, P. In case of a plane wave propagating ina non-dispersive homogeneous dielectric medium with a refractive indexn, this reference electromagnetic field quantity is defined as:

$\begin{matrix}{{P = {{{E_{m}^{2}/2}\; \eta} \approx {1.3\mspace{14mu} n\mspace{14mu} {E_{m}^{2}\mspace{14mu}\left\lbrack \frac{mW}{m^{2}} \right\rbrack}}}},} & (4)\end{matrix}$

where E_(m) is the amplitude of the E-field, η is the wave impedance inthe medium and n is the refractive index. In case of a host media withrefractive index n=1.49, the reference value of the power densitycharacterized by the time average Poynting vector is ˜1.94 mW/m2.

FIGS. 12b and 12c show how the transformation of the cavitycross-section, S, from the circular shape to rectangular and 8-shapecauses the formation of multi-beam near-field patterns with four(referenced 104) and two (referenced 103) nanojet beams, respectively.This beam-forming effect is related to the transformation of theboundary segments from a convex shape to a planar shape and then toconcave shape, respectively. The beams observed in FIGS. 12b and 12dhave a radiation angle similar to the one of the conical beam producedby the circular cylinder (FIG. 12a ). At the same time, the width of thebeams in terms of the azimuth angle is different. The larger theinternal angle of the concave segment of the cavity cross-sectionboundary, S, the narrower the beam and the higher the field intensity.In particular, the FIE for the two cavities presented in FIGS. 12b(square shape) and 12 c (8-shape) is equal to a factor of ^(˜)2.5 and^(˜)2.8, respectively.

Finally, FIG. 12d shows that a wide blade-like nanojet beam is generatedby the hollow rectangular cavity. This example demonstrates thepossibility to form wide beams that can be of interest for certainapplications requiring uniform illumination of narrow shaped areas.

The boundary curvature of the cavity is hence a tool for changing thenanojet beam shape, position and field intensity enhancement.

The same approach can be used to build more complex components withsymmetrical or non-symmetrical cross-sections producing an arbitrarynumber of identical or different nanojet beams.

Some of these exemplary embodiments are illustrated by FIG. 13, whichpresents a schematic drawing of the field intensity distribution in theimaging plane for three exemplary cylindrical cavities with differentcross-sections. More precisely, FIG. 13a shows a cavity 111 a with acircular cross-section, as already illustrated by FIG. 11a : the dashedarrows schematically show that nanojet beams originate from the bottomof this cavity 111 a. The ring 551 indicates the hot spots in thenear-field distribution formed due to these nanojet beams.

FIG. 13b shows a non-symmetric cavity 111 b, which cross-section in thexy-plane is somehow triangular, but with one of the three edges of thetriangle which is concave. Such a circa triangular cavity 111 b createsthree spots 552, 553 and 554, one of which (554) is enhanced, thanks tothe concave face.

FIG. 13c shows a cavity, which is arbitrary-shaped with five straight orconcave segments. Spots 555 to 559 indicate the hot spots in thenear-field distribution formed due to the nanojet beams originating fromthe base edge of the step, as schematically shown by the dashed arrows.The specific field distribution with five hot spots observed in FIG. 13cis linked to the specific shape of the edge line having five straight orconcave segments responsible for the formation of five independentnanojet beams.

FIG. 14 provides a schematic drawing for the implementation of such acomponent according to an embodiment of the present disclosure.

Such a device presents a multi-layer structure comprising:

-   -   a first layer 110 forming a substrate, which may be made in        glass or plastic for example;    -   a second layer of dielectric material 112 abutting the substrate        110;    -   a third layer forming a superstrate 113, on top of the        dielectric layer 112. The superstrate may be made in glass or        plastic for example. In the embodiment of FIG. 11, the same        material is used for the substrate 110 and the superstrate 113,        although this is not compulsory.

A cavity 111 of arbitrary cross-section is formed in the layer ofdielectric material 112. FIG. 14 offers a 3D-view of the cavity 111, aswell as both a side view and a top view of the component.

In an embodiment, the device of FIG. 14 is a planaroptically-transparent (e.g. glass) plate with embedded cylindricalmicro-cavities oriented to be orthogonal to its surface. Both thesubstrate 110 and the superstrate 113 are glass plates, and the layer112 of dielectric material is a thin film made in anoptically-transparent polymer like PMMA (Poly(methyl methacrylate)).

A manufacturing process of such a component may consist in, first,depositing a film 112 of desired thickness on the glass plate 110; thencavities 111 are created in this film 112 using any establishedmicrofabrication technique, e.g. optical or e-beam lithography. Finally,the structure is covered with another glass plate 113.

Hence, unlike existing analogs, such a component can be fabricated usingestablished planar fabrication technologies, thanks to its simpletopology and availability of dielectric materials with the requiredrefractive index.

FIGS. 15a to 15f illustrate side views of alternate embodiments to thecomponent of FIG. 14.

In FIG. 15a , the component is made of a single layer of dielectricmaterial 112. An abrupt change of the surface level of the layer ofdielectric 112 forms a step, which also induces a step of index for anincident wave reaching the component from the bottom, as air surroundingthe component has a lower refractive index than the dielectric material112. Hence, the complex electromagnetic phenomena described above inrelation to FIGS. 2 to 10 take birth, first by diffraction of the planeincident wave on the lower part 120 of the surface, and then byrefraction of the diffracted wave on the lateral part 121 of the step.

The component may also be immersed in another material than air, forexample another gas, or the lower part 120 of the surface may be incontact with any other substance having a lower refractive index thanthe dielectric material 112.

FIG. 15b illustrates another embodiment, according to which thecomponent comprises a single layer of dielectric material 112, in whichis formed a cavity as a through-hole: the height of the cavity thuscorresponds to the thickness of the dielectric layer 112.

FIG. 15c illustrates another embodiment, according to which thecomponent comprises a single layer of dielectric material 112, in whichis formed a cavity 111, which height is smaller than the thickness ofthe layer of dielectric material 112. Both the height of the cavity andits cross-section may be arbitrarily chosen, as a function of the beamto be produced by the component. Notably, the top of the cavity need notnecessarily correspond to the top surface of the dielectric layer 112.

A specific embodiment in which the cavity 111 is of infinite dimensionscorresponds to the embodiment of FIG. 15a , the step corresponding to anedge of cavity 111.

FIG. 15d illustrates yet another embodiment, according to which thecomponent presents a double-layer structure, namely a first layer 110forming a substrate, on top of which is placed a second layer 112 ofdielectric material. A cavity 111 is formed in the layer 112 ofdielectric material. A specific embodiment, where the first layer 110and the second layer 112 are made in the same material, corresponds tothe embodiment of FIG. 15 c.

FIG. 15e corresponds to yet another embodiment, in which the devicepresents a three-layer structure, as in the embodiment of FIG. 14.However, the substrate 110 and the superstrate 113 need not necessarilybe made in the same material.

FIG. 15f illustrates yet another embodiment, in which the componentcomprises a set of two or more cavities formed in the layer ofdielectric material. The cavities may be arranged in regular arrays, orgrouped in any number and any pattern depending on the beam(s) to begenerated. Such multiple cavities may be formed in any of thesingle-layer or multi-layer embodiments of FIGS. 15b to 15 e.

Such an embodiment will be described in greater detail in theforthcoming in relation to FIGS. 17 to 23.

FIG. 16 illustrates a typical use scenario of the devices of FIGS. 14and 15. For sake of simplicity, the component illustrated in FIG. 16corresponds to the component of FIG. 14; it must be understood, however,that it may be replaced by any component corresponding to any of theembodiments of FIG. 15 as well.

An emitting element 130 emits a plane electromagnetic wave towards thebase surface of the device 132. The emitting element 130 can be either apart of the system (e.g. like in AR/VR glasses) or just a model of anexternal light source (e.g. scattered ambient light collimated by anobjective lens, like in case of a photo camera). For example, theemitting element 130 may be:

-   -   ambient light coming from a source located far away;    -   light produced by a light source directly attached to the        nanojet component 132 (e.g. photodiode or optical fiber);    -   optical beam produced by another focusing element 132.

It can be located at any distance from the cavity 111 and generate adirective light beam or an omnidirectional light emission.

Depending on the design and fabrication method, the structure of device132 may consist of two or more layers sealed together, as explainedabove in relation to FIG. 15. In the embodiment of FIG. 16, such adevice presents a three-layer structure with one or severalmicrocavity(ies) 111 on one or both surfaces of the sealed substrate 110and superstrate 113. In some embodiments, this structure of device 132may be directly attached to either the emitting element 130 and/orreceiving element 131. For example, it may take the form of a flexiblecomponent directly placed on a sensor or a plano-convex lens.

The cavity or cavities 111 are hollow (hence filled with air), or filledwith a material with a refracting index lower than that of the substrate110.

A receiving element 131 must be located within a certain distance fromthe cavity that depends on the length of the nanojet beam generated bythe cavity. This distance can generally vary from about 3 to 10wavelengths. The dashed circle in FIG. 16 indicates the maximum distanceR_(max) to the receiving element 131. It can be larger for certainarrangement of cavities, comprising more than one cavity (see below inrelation to FIGS. 17 to 23). The possible relative positions of thecavity, emitting and receiving elements are defined by the nanojet beam55 radiation angle and the angle of incidence of the incoming wave.

The receiving element 131 may be:

-   -   a detector, e.g. photodiode in a camera,    -   a target, e.g. quantum dots, nanoparticles or molecules inside a        water or blood solution {spectroscopy, microscopy or lab-on-chip        device},    -   another focusing, beam-forming or light-guiding element, e.g.        lens, grating, optical fiber, AR/VR glasses, light        communication, etc.

As the component 132 according to the present disclosure may be used,either for generating beams 55 from incident plane wave, or forgenerating locally plane waves from incident non-planar waves or beams,the receiving 131 and emitting elements 130 may be reversed.

Such components 132 can be used as building blocks of integrated opticalsensors and/or light-guiding and light-processing systems, as well asstand-along focusing devices (e.g. a near-field probe). They are capableof near-field focusing with a subwavelength resolution and fieldintensity enhancement (FIE) of at least a factor of two, operating inthe optical range.

FIG. 17 illustrates a specific embodiment of the present disclosure,according to which the focusing component is based on a 2×2 array ofhollow cuboids embedded in a host medium. FIG. 17a illustrates thetopology of such a component, while FIG. 17b provides simulation resultsof the time-averaged power distribution when the component isilluminated by a unit-amplitude plane wave propagating along z-axis(n₁=1.49, L_(x)=L_(y)=L_(z)=2λ₁, S=0.5λ₁).

The component of FIG. 17a comprises four hollow cuboids (n₂=1) 140embedded in an optically transparent host medium 112 with refractiveindex n₁>n₂. For instance, this can be a glass, plastic (e.g. PMMA), orpolymer (e.g. PDMS (Polydimethylsiloxane)).

A nanojet beam is generated on the axis of the 2×2 array of hollow(n₂=1) cuboids 140 embedded in a homogeneous dielectric medium 112 witha refractive index n₁=1.49 that is a typical value for glass andplastics in the optical range. Analysis shows that, by optimizing thesize, shape and relative positions of the cuboids with respect to thehost medium refractive index and wavelength of the incident plane wave,a nanojet beam can be generated with the beam full width at half power(FWHP) of ^(˜)λ/2n₁ and FIE of at least a factor of 5.

FIG. 18 illustrates an alternate embodiment, in which the hollowrectangular cuboids 140 are replaced with hollow cylinders 141, orientedalong the plane wave propagation direction. As in FIG. 17, FIG. 18aillustrates the topology of such a component, while FIG. 18b providessimulation results of the time-averaged power distribution when thecomponent is illuminated by a unit-amplitude plane wave propagatingalong z-axis (n₁=1.49, L_(z)=2λ₁, R=λ₁, S=0.5λ₁).

The cylindrical shape facilitates manufacturing procedure, thanks toelimination of sharp vertical edges of the cuboids. In particular, suchcylindrical apertures can be fabricated via optical lithography oranother established planar micro-fabrication technology, likenanoimprinting or replica molding.

FIG. 19 illustrates yet another embodiment, in which a 2×2 array ofhollow cylinders 141 is created at the boundary of the dielectric medium112 and free space, e.g. on the surface of a glass or plastic plate.When illuminated by a plane wave from the media side, such a componentproduces a nanojet beam in free space close to the surface of the plate112. This embodiment can be advantageous for applications that requirean air gap between the focusing component and the object under test thatis a typical scenario for optical data storage, microscopy,spectroscopy, and metrology systems.

As in FIG. 18, FIG. 19a illustrates the topology of such a componentbased on a 2×2 array of hollow cylinders created at the interface of thedielectric medium and free space, while FIG. 19b provides simulationresults of the time-averaged power distribution when the component isilluminated by a unit-amplitude plane wave propagating along z-axis(n₁=1.49, Lz=2λ₁, R=λ₁, S=0.5λ₁).

The profiles of the nanojet beams produced by all three embodiments ofFIGS. 17, 18 and 19 are illustrated in FIG. 20. The profiles are plottedin terms of field intensity enhancement (FIE) defined with respect tothe field intensity of the plane wave propagating in the same hostmedia. More precisely, in FIG. 20a one can see the beam profiles alongz-axis, whereas FIGS. 20b-20c-20d show the beam cross-sectional view inthe plane z=z_(m), where z_(m) is a point with the maximum fieldintensity derived from FIG. 20a . As may be observed, the subwavelengthresolution is well preserved for all three embodiments, whereas the FIEvaries in the range of about 5 to 11 a.u. Note that in all cases, FIE isdefined as a ratio between the field intensity level in a given pointwith and without a focusing device according to embodiments of theinvention, with respect to the unit-amplitude plane wave propagating inthe same host medium, namely glass (embodiments of FIGS. 17 and 18) andfree space (embodiment of FIG. 19).

Additional analysis shows that the focal spot position along z-axis canbe changed within a certain range by varying size and spacing betweencuboids (cylinders). The possibility of changing the nanojet beam lengthand position can be of interest for applications that require in-depthscanning or imaging.

FIG. 21 provides two additional exemplary embodiments based onsingle-periodic (FIG. 21a ) and double-periodic (FIG. 21b ) arrays ofhollow cylinders 141 embedded in a host medium 112. In both embodiments,the hollow cylinders form a number of regularly-spaced sub-arrays of 2×2closely-positioned scatterers that act like the component illustrated inFIG. 18. Note that in case of FIG. 21b , each hollow cylinder 141simultaneously contributes to the formation of four nanojets.

The embodiments of FIG. 21 can be of interest for systems that canbenefit from a multi-spot focusing capability. For instance, it could becameras or spectroscopy systems.

Of course, in all the embodiments described above, the shape of thecavities is not restricted to regular cylinders or cuboids. As explainedin relation to FIGS. 2 to 10, the electromagnetic phenomena highlightedby the inventors of the present disclosure will occur for any shape ofcavity, whether cone-shaped, a prism, or a cylinder (in the broad senseof the term, i.e. a surface created by projecting a closedtwo-dimensional curve along an axis intersecting the plane of thecurve), and whatever its cross-section. Moreover, the main axis of thecavity may be orthogonal to the surface of the dielectric material orthe substrate, or may be tilted with any angle with respect to thissurface.

FIG. 22 is a schematic drawing illustrating a possible implementationembodiment for the periodic structures of FIGS. 21a and 21 b.

The proposed component, in all its embodiments, can be, for instance,fabricated in the form of a thin film with perforated apertures attachedto a glass plate or directly to a flat surface of another opticalcomponent, such as a plano-convex lens. For the embodiments of FIGS. 17,18, 19, and 21, it can then be covered with another layer of anoptically-transparent media (e.g. another glass plate).

The film can be made of an optically transparent material, like PMMA(Acrylic), that is to be deposited directly on the surface of thesupporting component (e.g. glass plate or lens). For instance, this canbe done by spin-coating that enables deposition of thin nanofilms withthe desired thickness (order of a few hundred nanometers).

The apertures (that will serve as hollow cuboids) can then be created,for instance, using the optical or e-beam lithography technology.

The periodic structures can be, potentially, fabricated using themaskless interference lithography that is faster and cheaper thanstandard optical lithography.

FIG. 23 presents an alternate possible implementation embodiment for theperiodic structures of FIGS. 21a and 21 b.

In this alternate implementation, the hollow cuboids can be fabricatedusing nanoimprinting or replica molding methods in an opticallytransparent material, e.g. soft organic polymer such as PDMS, and thenattached to a surface of a glass plate acting as a support.

The manufacturing processes described in relation to FIGS. 22 and 23 aregiven as mere examples, in order to highlight the fabricationfeasibility of the device according to the present disclosure, usingestablished microfabrication methods. However, some other manufacturingmethods may also exist, or be better suited for a mass production.

A new method and a set of components for near-field focusing andbeam-forming have been presented.

The components have a form of conical, prismatic or cylindricalcavities, whose cross-sections are shaped to produce a different numberof nanojet beams with adjustable repartition and outline.

The shape and arrangement of the nanojet beams in xy-plane and theirextension in z are defined by the shape of the cavity cross-section.More generally, a simple step in the surface of a dielectric layer isenough for generating such nanojet beams.

The length of the beam depends on the cavity size and index ratio.

For a given index ratio, the main parameters (i.e. length, width, angleof radiation, and FIE) remain stable in the wavelength range of at least±20%.

Such components provide numerous advantages, as compared to prior artfocusing devices, among which:

-   -   a simple topology, which may be planar, or flexible, and        provides a good mechanical rigidity;    -   they are based on standard materials, and hence can be        fabricated using standard dielectric materials, like optical        glasses or plastics. There is no need for high-index materials        (unlike for prior art SDC);    -   a simple fabrication: they can be manufactured using established        planar microfabrication methods, such as laser and e-beam        lithography, nanoimprinting, replica molding, etc.    -   a simple integration: they can either be used as stand-along        components (e.g. near-field probe), or attached to other optical        components (e.g. plano-convex lens), or used as a building        blocks of an integrated focusing system (e.g. camera sensors);    -   good performance characteristics, with a subwavelength        resolution of ^(˜)λ/2n₁ (i.e. one-half of the wavelength in the        host medium) and a FIE of a factor of 2 to at least 11.

It should be noted that in one embodiment of the disclosure, the presenttechnique may not be limited to the non-radiative (reactive) zone butcan also comprise the Fresnel radiative, the transition, and partly thefar-field zones.

1. A device for forming a field intensity distribution in the near zone,from propagating electromagnetic waves which are incident on saiddevice, wherein said device comprises: at least one layer of dielectricmaterial, having a first refractive index n1 with a surface having atleast one abrupt change of level forming a step; an element having asecond refractive index n2 lower than said first refractive index n1,which is in contact with said step; and wherein said step generates abeam which is tilted compared to a propagation direction of saidelectromagnetic waves.
 2. The device of claim 1, wherein said titledbeam has a length that can vary from ½ λ_1 to several wavelengths, withλ_1 being a wavelength of said electromagnetic waves in said dielectricmaterial.
 3. The device of claim 1, wherein it comprises a receivingelement positioned along a propagation direction of said titled beam. 4.The device of claim 3, wherein said receiving element is positioned at ahot spot of said beam.
 5. The device of claim 3, wherein said receivingelement is positioned at a distance d from said step, where d is betweenone λ_1 to 10λ_1, with λ_1 being a wavelength of said electromagneticwaves in said dielectric material.
 6. The device of claim 1, whereinsaid titled beam is associated with an angle of radiation which isdefined as a function of said first refractive index n1 and/or saidsecond refractive index n2, and/or incident angles of said incidentelectromagnetic waves compared to said step, and/or a step base angle.7. The device of claim 6, wherein said angle of radiation is around avalue equal to (90°−a sin(n2/n1))/2.
 8. The device of claim 7, whereinsaid angle of radiation is around 23° when n1=1.49 and n2=1, and around30°, when n1=2 and n2=1.
 9. The device of claim 1, wherein it is adaptedto form beams for incident electromagnetic waves that are monochromaticelectromagnetic waves, each of said monochromatic electromagnetic waveshaving a wavelength equal to a value which is around 480 nm or 525 nm or650 nm.
 10. The device of claim 1, wherein said step is formed by anedge of at least one cavity made in said at least one layer ofdielectric material.
 11. The device of claim 10, wherein said at leastone cavity is a through-hole in said at least one layer of dielectricmaterial.
 12. The device of claim 10, wherein said at least one cavitybelongs to at least one set of at least two cavities.
 13. The device ofclaim 10, wherein said at least one cavity is targeted to be cylindricalor cone-shaped.
 14. The device of claim 1, wherein a height H of saidstep is targeted to be such that H>λ_½, where λ_1 is a wavelength ofsaid electromagnetic waves in said dielectric material.
 15. The deviceof claim 2, wherein it also comprises at least one layer forming asubstrate abutting said layer of dielectric material.
 16. The device ofclaim 15, wherein it also comprises at least one layer forming asuperstrate, said at least one layer of dielectric material beinglocated between said substrate and said superstrate.
 17. The device ofclaim 16, wherein said substrate and said superstrate are made of thesame dielectric material as said at least one layer of dielectricmaterial.
 18. The device of claim 1, wherein said dielectric materialbelongs to the group comprising: glass; plastic; a polymer material. 19.The device of claim 16, wherein a material of said superstrate belongsto the group comprising: glass; plastic; a liquid; a polymer material.